Question

k for the individual \spring\ (rubber band) can be determined with a \fishing scale\ (weighs in grams or hectograms). be sure that the scale reads zero when theres no mass attached. follow the procedure, below.
procedure:

1. loop a rubber band around the backstop board and c - clamp the backstop into place.
2. attach the other end of the rubber band to the fishing scale. use a meter stick to measure a stretch of the rubber band a distance $\delta x = 0.30$ m (30 cm).
3. observe the reading on the scale - should be around 6 hectograms (600 grams or 0.6 kg). convert this mass to kilograms.
4. next, use newtons 2nd law for gravity $f = m\cdot g$ whenever you must convert mass m to force f.
5. using $f = -k\cdot \delta x$, a little algebra, and the fishing scale find k.

Explanation:

Step1: Convert mass to kg

Given mass \( m = 0.6 \, \text{kg} \) (from 600 grams).

Step2: Calculate force using \( F = m \cdot g \)

Take \( g = 9.8 \, \text{m/s}^2 \). So \( F = 0.6 \times 9.8 = 5.88 \, \text{N} \).

Step3: Use Hooke's Law \( F = k \cdot \Delta x \) (magnitude, so ignore sign)

Given \( \Delta x = 0.30 \, \text{m} \). Rearrange for \( k \): \( k=\frac{F}{\Delta x} \).

Step4: Substitute values

\( k = \frac{5.88}{0.30} = 19.6 \, \text{N/m} \).

Answer:

The spring constant \( k \) of the rubber band is \( \boldsymbol{19.6 \, \text{N/m}} \) (or approximately \( 20 \, \text{N/m} \) if using \( g = 10 \, \text{m/s}^2 \)).